A power grid power quality time sequence probability evaluation method, system and device

Abstract

The application discloses a power grid power quality time sequence probability evaluation method, system and device, relates to the power system power quality evaluation technical field, and the method comprises the following steps: acquiring the measured historical data of electrified railway traction load and a wind power plant, and constructing a non-parametric time sequence probability model; sampling is generated from the non-parametric time sequence probability model; an asymmetric three-phase power flow calculation model containing a traction power supply system is established; the time sequence probability sample is input into the three-phase power flow calculation model, and the time sequence probability distribution of three-phase voltage amplitude and three-phase voltage unbalance degree of each node in the power grid is obtained; based on the shapley value theory, the marginal contribution degree of power injection of each node to the voltage quality index is quantified, and quantitative evaluation of power quality is completed; the method overcomes the problem that the traditional static probability model cannot reflect the dynamic evolution trend of the system, and the evaluation result truly reflects the time period change law of the system in actual operation.

Description

Technical Field

[0001] This invention relates to the field of power system power quality assessment technology, specifically to a method, system, and device for time-series probability assessment of power grid power quality. Background Technology

[0002] With the rapid development of electrified railways and the large-scale grid connection of wind power, a large number of traction loads and wind power with randomness, volatility, and intermittency have emerged in the power system. Electrified railway traction loads, as typical single-phase high-power impulsive loads, generate negative-sequence currents during operation that significantly disrupt the three-phase balance of the power grid, leading to excessive voltage imbalance. Meanwhile, wind farm output is affected by meteorological factors such as wind speed and direction, exhibiting strong randomness and temporal correlation; its power fluctuations further exacerbate the amplitude deviation and imbalance of the grid voltage. The superimposed effect of these two types of elements on a time scale gives the evolution of power quality problems in the power grid a distinct dynamic temporal characteristic.

[0003] Currently, traditional power quality assessment methods are mostly based on steady-state or static probabilistic models, typically assuming that the power of loads and power sources follows a fixed probability distribution, and using this to calculate the statistical characteristics of system node voltages, imbalances, and other indicators. However, these methods neglect the intraday load variation patterns of electrified railway train operations and the continuous fluctuations in wind power output due to diurnal variations, failing to depict the continuous evolution of the system's operating state over different time periods. Therefore, assessment results obtained using static models often deviate from reality and cannot truly reflect the dynamic evolution of the system during actual operation. Other research has explored power quality assessment methods based on time-series probabilistic models, simulating the system's operating state at different time periods by introducing time-dimensional sample generation and power flow calculations; however, these methods, focusing on modeling a single type of disturbance source, do not adequately consider scenarios involving the combined effects of multiple uncertainties, such as those from electrified railways and wind power.

[0004] In summary, existing methods do not fully consider the temporal variation patterns of traction load and wind power, making it difficult for the evaluation results to truly reflect the dynamic behavior and evolution trend of the system during actual operation. Summary of the Invention

[0005] To address the problem that existing technologies do not fully consider the temporal variation patterns of traction load and wind power, resulting in assessment results that fail to accurately reflect the dynamic behavior and evolution trend of the system during actual operation, this invention proposes a temporal probability assessment method, system, and device for power grid power quality, thereby solving the problems existing in the prior art.

[0006] A time-series probabilistic method for assessing power quality in a power grid includes the following steps: Obtain measured historical data of traction load nodes of electrified railways and wind farm nodes in the power grid; Based on measured historical data, nonparametric time-series probabilistic models for traction load and wind power were constructed respectively; and time-series probabilistic samples of traction load and wind power were generated by sampling from the nonparametric time-series probabilistic models using the time-series Latin hypercube sampling method. For the voltage on the two-phase side of the traction transformer in an electrified railway, the two-phase voltage is transformed to the three-phase side using a two-phase to three-phase voltage transformation matrix, a current transformation matrix, and their inverse matrices, to obtain the three-phase equivalent impedance matrix of the traction transformer. Based on the equivalent impedance matrix, an equivalent three-phase admittance matrix of the traction transformer is established. This equivalent three-phase admittance matrix is ​​then incorporated into the original node admittance matrix of the power grid to generate an asymmetric three-phase power flow calculation model containing the traction power supply system. Time-series probability samples are input into the three-phase power flow calculation model to solve for the time-series probability distributions of the three-phase voltage amplitude and the three-phase voltage imbalance at each node in the power grid. The power injection of each node in the power grid participating in the power flow calculation is taken as the set of participants in the cooperative game. The scalarized voltage quality index extracted from the time series probability distribution is used as the alliance payoff function. Based on the Shapley value theory, the marginal contribution of each node's power injection to the voltage quality index is quantified, and the power quality of the power grid is quantitatively evaluated.

[0007] Furthermore, based on measured historical data, nonparametric time-series probabilistic models for traction load and wind power are constructed using adaptive kernel density estimation, specifically including the following steps: The measured historical data were divided into equal time periods, and a time series sample set of each random variable was constructed within the corresponding time period. An adaptive kernel density estimation method is used to fit the probability density function of the time series samples for each time period. The kernel bandwidth is automatically adjusted to accurately characterize the impact of load fluctuations and the multi-peak, non-normal distribution of wind power output. The final nonparametric time series probability model is then obtained, expressed as: ; Wherein, the kernel function is ; This represents the number of measured power data points. Indicates power variable; Indicates the first Power data; optimal bandwidth The error is determined adaptively by minimizing the mean square integral error.

[0008] Furthermore, the method of using temporal Latin hypercube sampling to sample and generate temporal probability samples of traction load and wind power from a nonparametric temporal probability model specifically includes the following steps: Set the sampling scale parameters and the total number of time periods for each time period; divide the cumulative probability distribution of traction load and wind power in each time period into multiple equal probability zones; In each equally probable interval, a uniformly random number is generated independently as the sampling probability; The sampling probability is converted into the corresponding power sample value by using the inverse cumulative distribution function; Multiple power sample values ​​generated for each variable are randomly combined to form a time-series probability sample for that period.

[0009] Furthermore, the process of constructing the equivalent three-phase admittance matrix of the traction transformer specifically includes the following steps: Establish the voltage equations for the two phases of the traction transformer: ; Among them, among them, , These are the ports of the traction transformer. and port The equivalent power source electromotive force; , These are the ports of the traction transformer. and port The actual output voltage; , They are respectively Winding and Equivalent self-impedance of the winding; , yes Winding and The equivalent mutual impedance between windings reflects the electromagnetic coupling between two phase windings; , These are the ports. and port The current, i.e. the current flowing from the transformer to the traction load and the filter / compensation device; Through two-phase to three-phase voltage transformation matrix and current transformation matrix Its inverse matrix transforms the two-phase voltage to the three-phase voltage: ; in, This is the three-phase equivalent impedance matrix of the traction transformer; This is the column vector of the three-phase electromotive force on the grid side; This is the column vector of the actual three-phase terminal voltages on the grid side; This represents the column vector of three-phase currents on the grid side. The equivalent three-phase admittance matrix obtained based on the three-phase equivalent impedance matrix is: .

[0010] Furthermore, the three-phase admittance matrix is ​​incorporated into the original node admittance matrix of the power grid, and an asymmetric three-phase power flow calculation model including the traction power supply system is established using the phase component method, specifically expressed as follows: ; in, and Represent any phase of A, B, and C; and Representing nodes respectively exist The imbalance between active and reactive power in a phase; and Representing nodes respectively exist Given the injected active and reactive power; For nodes of Phase voltage amplitude; For nodes of Phase voltage amplitude; For nodes of Phase and node of Phase voltage phase angle difference; and These are the real and imaginary parts of the system's three-phase node admittance matrix, respectively. This represents the number of nodes in the system.

[0011] Furthermore, the step of inputting time-series probability samples into the three-phase power flow calculation model to solve for the time-series probability distributions of the three-phase voltage amplitude and three-phase voltage imbalance at each node in the power grid specifically includes the following steps: By setting the convergence accuracy threshold and the maximum number of iterations for the Newton-Raphson iterative method, the three-phase node admittance matrix and the initial value of the node voltage are obtained. Traverse each time period, and within each time period, traverse all sampling scenarios. Use the traction load power value and wind power value in the time series probability sample as the injection boundary conditions of the corresponding node, and perform deterministic three-phase power flow calculations in sequence. Use the Newton-Raphson method to iteratively solve the voltage amplitude and phase angle of each phase of each node. For each converged power flow calculation result, calculate the three-phase voltage imbalance at each node: ;in, It is the positive sequence component of voltage. It is the negative sequence component of voltage; Statistical analysis was performed on the voltage amplitude and voltage imbalance calculation results of all sampling scenarios in each time period to obtain the time-series probability distribution of the three-phase voltage amplitude and three-phase voltage imbalance of each node.

[0012] Furthermore, the method of quantifying the marginal contribution of power injection at each node to voltage quality indicators based on Shapley value theory, thereby completing a quantitative assessment of power grid quality, is specifically expressed as follows: Define the set of participants N This includes traction load nodes and wind farm nodes; defining voltage quality index value functions. For any subset S ⊆ N In the subset S Timing probabilistic power flow calculations are performed under the corresponding boundary conditions to extract the target node voltage quality scalarization index as the function value; The Shapley value for each participant was approximated using Monte Carlo sampling. : ; in, Inject power into the node; For nodes The power; For without A subset of; This refers to the number of system nodes. This is a function of the voltage quality index value; Through multiple Monte Carlo simulations, the moving average of the Shapley value is monitored in real time during the simulation process. Convergence is determined when the change is less than a preset threshold. The average of the simulation results is used as the final Shapley value estimate. Based on the sign and magnitude of the Shapley value, determine the direction and extent of the impact of power injection at each node on voltage quality indicators.

[0013] The present invention also includes a power grid power quality time-series probabilistic assessment system, comprising: The acquisition module is used to acquire measured historical data of traction load nodes of electrified railways and wind farm nodes in the power grid; The sampling module is used to construct nonparametric time-series probability models of traction load and wind power based on measured historical data; and to use the time-series Latin hypercube sampling method to sample and generate time-series probability samples of traction load and wind power from the nonparametric time-series probability models. The power flow calculation module is used to transform the voltage on the two-phase side of the traction transformer in electrified railways to the three-phase side using a two-phase to three-phase voltage transformation matrix, a current transformation matrix, and their inverse matrices, to obtain the three-phase equivalent impedance matrix of the traction transformer. Based on the equivalent impedance matrix, an equivalent three-phase admittance matrix of the traction transformer is established. This equivalent three-phase admittance matrix is ​​then incorporated into the original node admittance matrix of the power grid to generate an asymmetrical three-phase power flow calculation model containing the traction power supply system. Time-series probability samples are input into the three-phase power flow calculation model to solve for the time-series probability distribution of the three-phase voltage amplitude and the three-phase voltage imbalance at each node in the power grid. The evaluation and analysis module is used to take the power injection of each node in the power grid participating in the power flow calculation as the set of participants in the cooperative game, and to take the scalarized voltage quality index extracted from the time series probability distribution as the alliance payoff function. Based on the Shapley value theory, it quantifies the marginal contribution of each node's power injection to the voltage quality index, and completes the quantitative evaluation of the power grid's power quality.

[0014] The present invention also includes a computer device for time-series probabilistic assessment of power grid power quality, comprising: a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the power grid power quality time-series probabilistic assessment method.

[0015] The present invention also includes a readable storage medium storing a computer program, the computer program including program instructions, which, when executed by a processor, are used to perform the steps of the power grid power quality time-series probability assessment method.

[0016] This invention provides a time-series probabilistic assessment method for power quality in power grids, which has the following beneficial effects: This invention constructs a nonparametric time-series probabilistic model of traction load and wind power, which can dynamically optimize the kernel bandwidth according to the data distribution characteristics. This overcomes the problems of strong assumptions and poor local adaptability of fixed-bandwidth kernel density estimation in traditional parametric models, significantly improving the ability to characterize complex distribution characteristics such as nonnormal, multi-peak, and spike distributions. By establishing a three-phase equivalent model of the traction transformer through a two-phase to three-phase transformation matrix and forming an asymmetrical three-phase power flow calculation model, this invention overcomes the problem that traditional single-phase or simplified three-phase models cannot accurately characterize the asymmetrical three-phase structure of the traction power supply system, providing reliable model support for the accurate evaluation of negative sequence voltage. Furthermore, by introducing Shapley value theory, each section... By treating point power injection as a cooperative game participant and voltage quality indicators as the alliance's gain, this method quantifies the marginal contribution of each uncertain power to the power quality indicators from a cooperative game perspective. This overcomes the problem that traditional qualitative or semi-quantitative analysis cannot reveal the differences in the contributions of various factors, and achieves a fair allocation and quantitative ranking of power quality influencing factors. Through the combination of the above technologies, this method overcomes the problem that traditional static probability models cannot reflect the dynamic evolution trend of the system. The evaluation results truly reflect the time-period variation law of the system in actual operation, and are more valuable for engineering reference. It can provide a scientific quantitative decision-making basis for the power quality governance of power grids with electrified railways and wind farms coupled together. Attached Figure Description

[0017] Figure 1 This is a flowchart illustrating the time-series probability assessment method for power quality in power grids according to an embodiment of the present invention. Figure 2 This is a schematic diagram of the V / x connection traction transformer wiring in an embodiment of the present invention; Figure 3 This is a three-phase equivalent model diagram of the traction power supply system in an embodiment of the present invention; Figure 4 This is a probability density diagram of traction load timing in an embodiment of the present invention; Figure 5 This is a temporal probability density diagram of a wind farm in an embodiment of the present invention; Figure 6 This is a probability density diagram of the three-phase voltage amplitude at each node in an embodiment of the present invention; Figure 7 This is a probability density diagram of the three-phase voltage imbalance at each node in this embodiment of the invention; Figure 8 This is a probability diagram of the three-phase voltage imbalance exceeding the limit at each node in this embodiment of the invention; Figure 9 This is a time-series graph showing the variation of the Shapley value of the voltage imbalance of the traction load in an embodiment of the present invention. Detailed Implementation

[0018] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments.

[0019] This invention proposes a time-series probabilistic assessment method for power grid power quality. This method constructs a time-series probabilistic model of traction load and wind power based on an adaptive kernel density estimation method; proposes a time-series Latin hypercube sampling method to generate time-series probabilistic samples of input random variables; establishes an asymmetric three-phase power flow model of the traction power supply system, wind power system, and power grid; introduces the Shapley value from game theory to quantify the impact of uncertain power on power quality; realizes the transformation of power quality assessment from static to time-series, accurately describes the degree of interaction between electrified railways and wind farms, provides accurate random variable probabilistic modeling, and offers fast calculation speed for three-phase time-series probabilistic power flow based on LHS, providing a methodological basis for power quality management in power grids containing electrified railways and new energy sources.

[0020] like Figure 1 As shown, the method specifically includes the following steps: S1. Analyze the measured historical data of traction load and wind power, remove the no-load data, and construct nonparametric time series probability models of traction load and wind power based on adaptive kernel density estimation.

[0021] Specifically, by acquiring measured historical data of electrified railway traction load and wind farms, and dividing the data into hourly time periods, a time series sample set for each random variable within the corresponding time period is constructed. Based on this, an adaptive kernel density estimation method is used to fit the probability density function of the samples in each time period, and the kernel bandwidth is automatically adjusted to accurately characterize the impact of the load and the multi-peak, non-normal distribution characteristics of wind power output.

[0022] The adaptive kernel density estimation obtains the optimal bandwidth by solving the following equation: ; in, For traditional KDE bandwidth, sensitivity coefficient A value of 0.5 is chosen to ensure optimal local adaptability; parameter As a global scaling factor, it is optimized through cross-validation to achieve a global balance between bias and variance.

[0023] The final AKDE probability density function estimation expression is: ; Wherein, the kernel function is ; It represents the power variable, i.e., active or reactive power; This represents the number of measured power data points. Indicates the first Power data; optimal bandwidth The error is adaptively determined by minimizing the mean square integral error, and the specific calculation formula is as follows: ; The formula for calculating the integral squared error is as follows: .

[0024] S2. Using the temporal Latin hypercube sampling method, temporal probability samples of traction load and wind power are generated by sampling from the temporal probability model of random variables in step S1.

[0025] Specifically, a temporal Latin hypercube sampling method is used to generate temporal probability samples from the temporal probability model of traction load and wind power constructed in step S1. This method, through hierarchical sampling and random sorting, achieves efficient coverage of the probability distribution of each time period while maintaining the original temporal correlation, ensuring that the generated sample sequence reflects both random fluctuation characteristics and temporal evolution patterns.

[0026] (1) Divide the interval: in the first interval Within a time period, the cumulative probability distribution of each random variable is divided into... There are two equally probable intervals.

[0027] (2) Determine the sampling probability: in the first... Within each interval, the sampling probability is ,in for A random number that is uniformly distributed within an interval.

[0028] (3) Convert to sample values: using the inverse cumulative distribution function The sampling probability is converted into a sample value.

[0029] (4) Random combination: the combination of variables The samples are randomly combined to form the input sample set for that time period.

[0030] By sampling the probability model for each time period, the probability sample matrix for each time period can be obtained.

[0031] In this embodiment, traction load and wind power do not show a significant statistical correlation, so they are treated as independent random variables and directly randomly combined after sampling. If there is a correlation between variables, the sampling order can be adjusted using methods such as Cholesky decomposition and equal probability transformation to introduce a preset correlation structure.

[0032] S3. Based on the two-phase to three-phase voltage and current transformation matrix, a three-phase model of the traction power supply system is established to couple the traction load with the regional power grid. Wind power can be equivalently injected into the grid as three-phase symmetrical power, thereby constructing a three-phase time-series power flow calculation model including the traction power supply system and wind power. The V / x connection diagram of the traction transformer is shown below. Figure 2 As shown.

[0033] Establish a three-phase equivalent model of the V / x connected traction transformer, such as... Figure 3 As shown. The traction transformer transforms three-phase voltage into two-phase voltage, and the voltage equations for its two-phase sides are as follows:

[0034] ; in, , These are the ports of the traction transformer. and port The equivalent power source electromotive force; , These are the ports of the traction transformer. and port The actual output voltage; , They are respectively Winding and Equivalent self-impedance of the winding; , yes Winding and The equivalent mutual impedance between windings reflects the electromagnetic coupling between two phase windings; , These are the ports. and port The current is the current flowing from the transformer to the traction load and the filter / compensation device.

[0035] Through two-phase to three-phase voltage and current transformation matrix , Its inverse matrix transforms the two-phase voltage to the three-phase side: ; in, This is the column vector of the three-phase electromotive force on the grid side; This is the column vector of the actual three-phase terminal voltages on the grid side; This is the three-phase equivalent impedance matrix of the traction transformer; This is the column vector of the three-phase currents on the grid side.

[0036] Based on the above equivalent impedance matrix, the equivalent three-phase node admittance matrix of the traction transformer can be obtained. By incorporating the three-phase node admittance matrix into the original node admittance matrix of the power grid according to the modification rules for node admittance matrices, the three-phase equivalent modeling of the traction power supply system can be completed.

[0037] An asymmetrical three-phase power flow calculation model for a traction power supply system is established using the phase component method: ; in, and Represent any phase of A, B, and C; and Representing nodes respectively exist The imbalance between active and reactive power in a phase; and Representing nodes respectively exist Given the injected active and reactive power; For nodes of Phase voltage amplitude; For nodes of Phase voltage amplitude; For nodes of Phase and node of Phase voltage phase angle difference; and These are the real and imaginary parts of the system's three-phase node admittance matrix, respectively. This represents the number of nodes in the system.

[0038] S4. Input the time-series probability samples of the random variables generated in step S2 into the three-phase time-series power flow calculation model constructed in step S3. Solve the three-phase time-series power flow equations using the Newton-Raphson method, and then calculate the three-phase time-series probabilistic power flow for each time period to obtain the time-series probability distribution of the output random variables of the three-phase time-series probabilistic power flow. Figure 4 , Figure 5 As shown.

[0039] This involves using the Newton-Raphson method to solve the power flow equations, iteratively solving the modified equations, and obtaining the corresponding correction amount in each iteration; specifically including: The corrected equations for the three-phase power flow equations in polar coordinates are as follows: ; in, , These represent the active and reactive power imbalance vectors of each node, respectively. , These are the correction vectors for the phase angle and magnitude of the voltage at each node; the Jacobian matrix... Element is . The elements are ; The elements are ; The elements are .

[0040] When the iteration is At this time, the unbalanced power equation is: ; The correction can be obtained by calculating the Jacobian matrix, and then the first... Calculation results: .

[0041] The convergence criterion is that the maximum value of the active and reactive power deviations at all nodes is less than the preset tolerance, and the iterative convergence accuracy is set to 10. -12 After performing deterministic power flow calculations on all time-series probability samples generated in step S2, the time-series probability density functions and over-limit probabilities of indicators such as the three-phase voltage amplitude and three-phase voltage imbalance of each node are statistically analyzed.

[0042] Specifically, the product generated in step S2 The time-series probability samples are sequentially input into the three-phase power flow calculation model established in step S3, and the power flow equations are solved iteratively using the Newton-Raphson method, with the iteration convergence accuracy set to 10. -12 For each time period Statistical analysis was performed on the subdeterministic power flow calculation results to obtain the time-series probability distributions of the three-phase voltage amplitude and three-phase voltage imbalance at each node, such as... Figure 6 , Figure 7 As shown.

[0043] Due to the characteristics of the traction transformer wiring and the two-phase power supply structure, zero-sequence current cannot flow; therefore, the system mainly exhibits negative-sequence imbalance characteristics. The formula for calculating the three-phase voltage negative-sequence imbalance is:

[0044] ; in, It is the positive sequence component of voltage. It is the negative sequence component of voltage.

[0045] S5. Combine the Shapley value theory with the three-phase time-series probabilistic power flow calculation model to establish the value function of voltage quality statistical indicators, calculate the marginal contribution of node injected power to voltage quality indicators, and output the voltage quality time-series probabilistic evaluation results.

[0046] Specifically, based on a cooperative game theory perspective, the power injection of each node is considered as a player in the game, and voltage quality indicators (such as expected voltage amplitude, standard deviation, and three-phase voltage imbalance) are considered as the alliance's payoff. The Shapley value theory is used to quantify the marginal contribution of each participant to the voltage quality indicators, achieving a fair allocation and quantitative assessment of the impact of uncertain power on power quality. The Monte Carlo sampling method is used to approximate the calculation of the Shapley value. :

[0047] ; in, Node power injection set; For nodes The power; For without A subset of; This represents the total number of system nodes. This is a function representing the voltage quality index value.

[0048] Since accurate calculation requires enumerating all node combinations, the computational complexity increases exponentially with the number of nodes. Therefore, this invention uses the Monte Carlo sampling method to approximate the Shapley value. The number of Monte Carlo simulations is set, and the moving average of the Shapley value is monitored in real time during the simulation. When the change is less than a preset threshold (e.g., 10), the value is considered the moving average. -4 The simulation is considered convergent when the result is within a certain range. The average of the simulation results is taken as the final Shapley value estimate.

[0049] The sign and magnitude of the Shapley value characterize the degree and magnitude of the node's contribution to improving or weakening voltage quality indicators. A positive Shapley value indicates that power injection at the node exacerbates voltage quality problems, while a negative value indicates an improvement effect.

[0050] Compared with the prior art, the present invention has the following significant advantages: (1) High modeling accuracy: Adaptive kernel density estimation is used to construct a nonparametric time series probability model of input random variables. It can dynamically optimize the kernel bandwidth according to the data distribution characteristics. Compared with the traditional kernel density estimation method, the root mean square error is reduced by more than 54%, and the mean absolute percentage error is reduced by more than 85%, which significantly improves the ability to characterize the complex distribution characteristics of traction load and wind power such as nonnormality and multi-peak.

[0051] (2) Accurate structural description: By using the two-phase to three-phase voltage and current transformation matrix, a three-phase equivalent model of the traction transformer is established, thereby forming a complete three-phase system model, which accurately reflects the three-phase asymmetry characteristics of the traction power supply system and provides reliable model support for the accurate assessment of power quality issues such as negative sequence voltage.

[0052] (3) High computational efficiency: The temporal Latin hypercube sampling method is used for probabilistic power flow calculation. Under the premise of ensuring computational accuracy, the computation time is only about 1 / 8 of that of traditional Monte Carlo simulation, which greatly reduces the computational cost and improves the engineering practicality and large-scale scene adaptability of the method.

[0053] (4) Quantification of evaluation results: By introducing the Shapley value theory, the node power injection is regarded as a game participant and the voltage quality index is regarded as the alliance benefit, so as to realize the quantitative decomposition and ranking of the power quality contribution of each node, and overcome the limitation of traditional qualitative analysis that it is difficult to quantify the contribution of influencing factors.

[0054] (5) Comprehensive time series characteristics: A 24-hour time series probability model is established to fully consider the intraday variation and periodic characteristics of traction load and wind power. The evaluation results can truly reflect the dynamic evolution process of the system in actual operation and are of greater engineering reference value.

[0055] (6) Strong engineering practicality: It can effectively identify key contribution nodes that affect power quality, providing scientific and quantitative decision-making basis for power grid planning, operation and control strategy formulation and power management equipment optimization configuration, and has strong practical application and promotion value.

[0056] Experimental verification To verify the effectiveness of the present invention, a simulation verification was performed using a modified IEEE-30 node three-phase system as an example.

[0057] 1. System Parameter Settings: Based on the IEEE-30 node example system on the MATLAB platform, a three-phase system model is established using the phase component method. The three-sequence parameters are converted to phase parameters, with negative sequence and positive sequence equal, and the zero-sequence impedance set to three times the positive sequence impedance. A traction transformer branch is connected at node 15, and the low-voltage side is named node 31. The traction load is connected to the traction transformer via a V / x connection (low-voltage side impedance...). ) and 10km line (positive sequence impedance) The system is connected to a three-phase balanced wind power source at node 26. The loads at other conventional nodes follow a normal distribution with a coefficient of variation of 10%.

[0058] The traction load has a high power factor, and the active power absorbed from the grid is used as the traction load, while the reactive power is negligible. The wind turbine adopts a direct-drive permanent magnet synchronous generator and uses a constant power factor control strategy to inject active and reactive power into the grid during normal operation.

[0059] 2. Data Acquisition and Preprocessing: To accurately obtain measured data on traction load and wind power, a Fluke 1760 data acquisition and analysis instrument was used to synchronously acquire electrical quantities of the α and β power supply arms of a traction substation on the Lanzhou-Xinjiang Railway. Simultaneously, a Dewesoft R2D power quality recorder was used to continuously record three-phase power data from a nearby wind farm. The sampling frequency of both devices was set to 10 kHz, meeting the accuracy requirements for power quality monitoring as specified in the IEC 61000-4-30 standard.

[0060] After acquiring the raw data, preprocessing was first performed to remove outlier samples, such as those under no-load conditions and those with impact characteristics, to ensure the representativeness and stability of the modeling data. Subsequently, the cleaned data was divided into 24 time periods by hour, and time-series probability models were constructed based on samples within each time period to characterize the dynamic changes in traction load and wind power across different time intervals throughout the day.

[0061] 3. Probabilistic Modeling Results Analysis: Taking the 14th time period as an example, AKDE was used to perform probabilistic modeling of traction load and wind power. The results show that the probability density curve of AKDE fits the histogram of measured data better than that of traditional KDE. The error index comparison is shown in the table below:

[0062] Table 1. Goodness-of-fit test results of the AKDE modeling method As shown in Table 1, the RMSE of AKDE for traction load decreased by 70.51% and the MAPE decreased by 21.24%. Meanwhile, the RMSE of AKDE for wind power decreased by 58.06% and the MAPE decreased by 73.65%, verifying the high accuracy of the AKDE method.

[0063] 4. Probabilistic Power Flow Calculation Efficiency Analysis: Three-phase probabilistic power flow calculations were performed using 500 NLHS runs and 5000 MCS runs respectively, and the calculation accuracy and efficiency were compared. The results show that the voltage probability density curve obtained by the NLHS method is in high agreement with that obtained by the MCS method, while the calculation time is only 9.8414 seconds, which is about 1 / 8 of that of the MCS method (82.7314 seconds), indicating a significant improvement in calculation efficiency.

[0064] 5. Voltage quality assessment results, such as Figure 8 As shown, during the peak traction load period (period 14), the probability of the three-phase voltage imbalance exceeding the limit at traction load node 31 is as high as 97.6314%, while the probability of the wind power node 26 exceeding the limit is only 12.3061%. The probability of the No. 5 busbar, which has a relatively long electrical distance, exceeding the limit is 0%.

[0065] 6. Shapley Value Evaluation Results: The Shapley value is used to quantify the contribution of traction load to the voltage imbalance at each node, such as... Figure 9 As shown. During the 14th time period, the Shapley value for the expected voltage imbalance of the traction load at node 31 is 1.767 × 10⁻⁶. -2 The Shapley value for node 15 is 1.408 × 10⁻⁶. -2 The Shapley value for the 26-node wind turbine bus is 1.054 × 10⁻⁶. -2 The Shapley value for busbar 5 is 3.866 × 10⁻⁶. -3 .

[0066] The Shapley values ​​are all positive, indicating that the traction load exacerbates the system voltage imbalance, and the impact is greater on nodes with closer electrical distances. This is consistent with the results of the physical mechanism analysis, verifying the effectiveness and accuracy of the method of this invention.

[0067] Based on the same inventive concept, this invention also proposes a time-series probabilistic assessment system for power grid power quality, comprising: The acquisition module is used to acquire measured historical data of traction load nodes of electrified railways and wind farm nodes in the power grid.

[0068] The sampling module is used to construct nonparametric time-series probability models for traction load and wind power based on measured historical data; and to use the time-series Latin hypercube sampling method to sample and generate time-series probability samples of traction load and wind power from the nonparametric time-series probability models.

[0069] The power flow calculation module is used to transform the voltage on the two-phase side of the traction transformer to the three-phase side using a two-phase to three-phase voltage transformation matrix and a current transformation matrix and their inverse matrices, thereby obtaining the three-phase equivalent impedance matrix of the traction transformer. Based on the equivalent impedance matrix, an equivalent three-phase admittance matrix of the traction transformer is established. This equivalent three-phase admittance matrix is ​​then incorporated into the original node admittance matrix of the power grid to generate an asymmetrical three-phase power flow calculation model containing the traction power supply system. Time-series probability samples are input into the three-phase power flow calculation model to solve for the time-series probability distribution of the three-phase voltage amplitude and the three-phase voltage imbalance at each node in the power grid.

[0070] The evaluation and analysis module is used to take the power injection of each node in the power grid participating in the power flow calculation as the set of participants in the cooperative game, and to take the scalarized voltage quality index extracted from the time series probability distribution as the alliance payoff function. Based on the Shapley value theory, it quantifies the marginal contribution of each node's power injection to the voltage quality index, and completes the quantitative evaluation of the power grid's power quality.

[0071] The present invention also proposes a computer device for time-series probabilistic assessment of power grid power quality, comprising: a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the time-series probabilistic assessment method for power grid power quality.

[0072] The present invention also proposes a readable storage medium storing a computer program, the computer program including program instructions, which, when executed by a processor, are used to perform steps of a power grid power quality timing probability assessment method.

[0073] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A time-series probabilistic assessment method for power quality in a power grid, characterized in that, Includes the following steps: Obtain measured historical data of traction load nodes of electrified railways and wind farm nodes in the power grid; Based on measured historical data, nonparametric time-series probabilistic models for traction load and wind power were constructed respectively; and time-series probabilistic samples of traction load and wind power were generated by sampling from the nonparametric time-series probabilistic models using the time-series Latin hypercube sampling method. For the voltage on the two-phase side of the traction transformer in an electrified railway, the two-phase voltage is transformed to the three-phase side using a two-phase to three-phase voltage transformation matrix, a current transformation matrix, and their inverse matrices, to obtain the three-phase equivalent impedance matrix of the traction transformer. Based on the equivalent impedance matrix, an equivalent three-phase admittance matrix of the traction transformer is established. This equivalent three-phase admittance matrix is ​​then incorporated into the original node admittance matrix of the power grid to generate an asymmetric three-phase power flow calculation model containing the traction power supply system. Time-series probability samples are input into the three-phase power flow calculation model to solve for the time-series probability distributions of the three-phase voltage amplitude and the three-phase voltage imbalance at each node in the power grid. The power injection of each node in the power grid participating in the power flow calculation is taken as the set of participants in the cooperative game. The scalarized voltage quality index extracted from the time series probability distribution is used as the alliance payoff function. Based on the Shapley value theory, the marginal contribution of each node's power injection to the voltage quality index is quantified to complete the quantitative assessment of the power grid's power quality.

2. The time-series probabilistic assessment method for power quality in a power grid according to claim 1, characterized in that, Based on measured historical data, nonparametric time-series probabilistic models for traction load and wind power are constructed using adaptive kernel density estimation, specifically including the following steps: The measured historical data were divided into equal time periods, and a time series sample set of each random variable was constructed within the corresponding time period. An adaptive kernel density estimation method is used to fit the probability density function of the time series samples for each time period. The kernel bandwidth is automatically adjusted to accurately characterize the impact of load fluctuations and the multi-peak, non-normal distribution of wind power output. The final nonparametric time series probability model is then obtained, expressed as: ； Wherein, the kernel function is ; This represents the number of measured power data points. Indicates power variable; Indicates the first Power data; optimal bandwidth The error is determined adaptively by minimizing the mean square integral error.

3. The time-series probabilistic assessment method for power quality in a power grid according to claim 1, characterized in that, The method employing time-series Latin hypercube sampling to sample and generate time-series probability samples of traction load and wind power from a nonparametric time-series probability model specifically includes the following steps: Set the sampling scale parameters and the total number of time periods for each time period; divide the cumulative probability distribution of traction load and wind power in each time period into multiple equal probability zones; In each equally probable interval, a uniformly random number is generated independently as the sampling probability; The sampling probability is converted into the corresponding power sample value by using the inverse cumulative distribution function; Multiple power sample values ​​generated for each variable are randomly combined to form a time-series probability sample for that period.

4. The time-series probabilistic assessment method for power quality in a power grid according to claim 1, characterized in that, The process of constructing the equivalent three-phase admittance matrix of the traction transformer specifically includes the following steps: Establish the voltage equations for the two phases of the traction transformer: ； Among them, among them, , These are the ports of the traction transformer. and port The equivalent power source electromotive force; , These are the ports of the traction transformer. and port The actual output voltage; , They are respectively winding and Equivalent self-impedance of the winding; , yes Winding and The equivalent mutual impedance between windings reflects the electromagnetic coupling between two phase windings; , These are the ports. and port The current, i.e. the current flowing from the transformer to the traction load and the filter / compensation device; Through two-phase to three-phase voltage transformation matrix and current transformation matrix Its inverse matrix transforms the two-phase voltage to the three-phase voltage: ； in, This is the three-phase equivalent impedance matrix of the traction transformer; This is the column vector of the three-phase electromotive force on the grid side; This is the column vector of the actual three-phase terminal voltages on the grid side; This represents the column vector of three-phase currents on the grid side. The equivalent three-phase admittance matrix obtained based on the three-phase equivalent impedance matrix is: .

5. The time-series probabilistic assessment method for power quality in a power grid according to claim 4, characterized in that, The three-phase admittance matrix is ​​incorporated into the original node admittance matrix of the power grid, and an asymmetric three-phase power flow calculation model including the traction power supply system is established using the phase component method, specifically expressed as follows: ； in, and Represent any phase of A, B, and C; and Representing nodes respectively exist The imbalance between active and reactive power in a phase; and Representing nodes respectively exist Given the injected active and reactive power; For nodes of Phase voltage amplitude; For nodes of Phase voltage amplitude; For nodes of Phase and node of Phase voltage phase angle difference; and These are the real and imaginary parts of the system's three-phase node admittance matrix, respectively. This represents the number of nodes in the system.

6. The time-series probabilistic assessment method for power quality in a power grid according to claim 1, characterized in that, The step of inputting time-series probability samples into the three-phase power flow calculation model to solve for the time-series probability distributions of the three-phase voltage amplitude and three-phase voltage imbalance at each node in the power grid specifically includes the following steps: By setting the convergence accuracy threshold and the maximum number of iterations for the Newton-Raphson iterative method, the three-phase node admittance matrix and the initial value of the node voltage are obtained. Traverse each time period, and within each time period, traverse all sampling scenarios. Use the traction load power value and wind power value in the time series probability sample as the injection boundary conditions of the corresponding node, and perform deterministic three-phase power flow calculations in sequence. Use the Newton-Raphson method to iteratively solve the voltage amplitude and phase angle of each phase of each node. For each converged power flow calculation result, calculate the three-phase voltage imbalance at each node: ;in, It is the positive sequence component of voltage. It is the negative sequence component of voltage; Statistical analysis was performed on the voltage amplitude and voltage imbalance calculation results of all sampling scenarios in each time period to obtain the time-series probability distribution of the three-phase voltage amplitude and three-phase voltage imbalance of each node.

7. The time-series probabilistic assessment method for power quality in a power grid according to claim 1, characterized in that, The method of quantifying the marginal contribution of power injection at each node to voltage quality indicators based on Shapley value theory to complete the quantitative assessment of power grid power quality is specifically expressed as follows: Define the set of participants N This includes traction load nodes and wind farm nodes; defining voltage quality index value functions. For any subset S ⊆ N In the subset S Timing probabilistic power flow calculations are performed under the corresponding boundary conditions to extract the target node voltage quality scalarization index as the function value; The Shapley value for each participant was approximated using Monte Carlo sampling. : ； in, Inject power into the node; For nodes The power; For without A subset of; This refers to the number of system nodes. This is a function of the voltage quality index value; Through multiple Monte Carlo simulations, the moving average of the Shapley value is monitored in real time during the simulation process. Convergence is determined when the change is less than a preset threshold. The average of the simulation results is used as the final Shapley value estimate. Based on the sign and magnitude of the Shapley value, determine the direction and extent of the impact of power injection at each node on voltage quality indicators.

8. A time-series probabilistic assessment system for power grid power quality, characterized in that, include: The acquisition module is used to acquire measured historical data of traction load nodes of electrified railways and wind farm nodes in the power grid; The sampling module is used to construct nonparametric time-series probability models of traction load and wind power based on measured historical data; and to use the time-series Latin hypercube sampling method to sample and generate time-series probability samples of traction load and wind power from the nonparametric time-series probability models. The power flow calculation module is used to transform the voltage on the two-phase side of the traction transformer in electrified railways to the three-phase side using a two-phase to three-phase voltage transformation matrix, a current transformation matrix, and their inverse matrices, to obtain the three-phase equivalent impedance matrix of the traction transformer. Based on the equivalent impedance matrix, an equivalent three-phase admittance matrix of the traction transformer is established. This equivalent three-phase admittance matrix is ​​then incorporated into the original node admittance matrix of the power grid to generate an asymmetrical three-phase power flow calculation model containing the traction power supply system. Time-series probability samples are input into the three-phase power flow calculation model to solve for the time-series probability distribution of the three-phase voltage amplitude and the three-phase voltage imbalance at each node in the power grid. The evaluation and analysis module is used to take the power injection of each node in the power grid participating in the power flow calculation as the set of participants in the cooperative game, and to take the scalarized voltage quality index extracted from the time series probability distribution as the alliance payoff function. Based on the Shapley value theory, it quantifies the marginal contribution of each node's power injection to the voltage quality index, and completes the quantitative evaluation of the power grid's power quality.

9. A computer device for time-series probabilistic assessment of power grid power quality, characterized in that, include: A memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the power grid power quality time-series probability assessment method according to any one of claims 1-7.

10. A readable storage medium, characterized in that, The readable storage medium stores a computer program, which includes program instructions that, when executed by a processor, perform the steps of the power grid power quality time-series probability assessment method according to any one of claims 1-7.

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